Theorem orbi1i 680

Description: Inference adding a right disjunct to both sides of a logical equivalence. (Contributed by NM, 5-Aug-1993.)

Hypothesis

Ref	Expression
orbi2i.1	|- ( ph <-> ps )

Assertion

Ref	Expression
orbi1i	|- ( ( ph \/ ch ) <-> ( ps \/ ch ) )

Proof of Theorem orbi1i

Step	Hyp	Ref	Expression
1		orcom 647	. 2 |- ( ( ph \/ ch ) <-> ( ch \/ ph ) )
2		orbi2i.1	. . 3 |- ( ph <-> ps )
3	2	orbi2i 679	. 2 |- ( ( ch \/ ph ) <-> ( ch \/ ps ) )
4		orcom 647	. 2 |- ( ( ch \/ ps ) <-> ( ps \/ ch ) )
5	1, 3, 4	3bitri 195	1 |- ( ( ph \/ ch ) <-> ( ps \/ ch ) )

Syntax hints:   <-> wb 98   \/ wo 629

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 630

This theorem depends on definitions:  df-bi 110

This theorem is referenced by:  orbi12i  681  orordi  690  dcan  842  3or6  1218  19.45  1573  sbequilem  1719  unass  3100  frecsuc  5991  elznn0nn  8259